F-Distribution

Probability · Axiom Academy

Ratio of chi-squared variables used in ANOVA and regression 1. Ratio of Chi-Squared Variables The F-distribution is constructed by taking two independent chi-squared random variables, dividing each by its degrees of freedom, then taking their ratio. This creates a distribution that's always positive and typically right-skewed. The distribution depends on both d₁ (numerator df) and d₂ (denominator df). The F-distribution is right-skewed and defined only for positive values. As both degrees of freedom increase, it becomes more symmetric. When d₂ is large, the distribution approaches a scaled chi-squared distribution. In ANOVA, the F-statistic compares between-group variability to within-group variability. Under the null hypothesis of equal group means, this ratio follows an F-distribution. The F-test also compares two sample variances and tests overall significance in regression.

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